Observation and background adjoint sensitivity in the adaptive observation-targeting problem

Recent observation-targeting field experiments, such as the Fronts and Atlantic Storm-Track EXperiment (FASTEX) and the NORth Pacific EXperiment (NORPEX), have demonstrated that by using objective adjoint techniques it is possible, in advance, to identify regions of the atmosphere where forecast-error growth in numerical forecast models is maximally sensitive to the error in the initial conditions. Typically such techniques produce a field of the sensitivity of some aspect of the forecast to the analysis field. This analysis sensitivity field is then used to identify promising targets for the deployment of additional observations during the flight-planning phase of field experiments. While FASTEX and, particularly NORPEX had a number of successful 'hits', where the addition of dropsondes reduced the forecast error, there were also failures. None of the objective techniques have involved any consideration of the characteristics of the data-assimilation systems used in the analysis of the targeted observations. In particular, the interaction with the background field, interactions with other observations, and the background- and observation-error characteristics have been ignored. This can lead to potential mis-sampling, conflict with other observations, and inefficient use of aircraft and expendables. In this study, the adjoint of a simplified data-assimilation system is used to determine directly the sensitivity of the forecast aspect to the observations and the background field. The procedure is illustrated by using simplified linear contexts such as the one- and two-dimensional horizontal univariate problem and the one-dimensional direct radiance assimilation problem. Adaptive targeting tools, such as a single-observation sensitivity map and a marginal observation sensitivity vector, are devised and tested. The possibility of determining when the forecast would be sensitive to the background field and/or the observations is demonstrated. Such dependencies are shown to be a function of the specified observation- and background-error variances, the characteristic scales of analysis sensitivity vector and background-error correlations, and the properties of forward (observation) operators. Although the present experiments concerned simplified assimilation systems and observation networks, extension of the technique to real situations is quite feasible. Obtaining the adjoint of a full three-dimensional variational assimilation system is straightforward; moreover, the target areas are small and contain relatively few observations so the computational requirements are modest. Finally, the data-assimilation adjoint theory can be used for a posteriori assessment of those sources of forecast error which are due to errors in the initial analysis.